具有水平对称轴的横向各向同性线性粘弹性介质波场特征

根据具有水平对称轴的横向各向同性 (HTI)线性粘弹性介质特征 ,推导出了本构关系式。使用平面均匀简谐波的方法 ,得到了Christoffel方程 ,利用此方程推导出纵波及快、慢横波的慢度和复速度方程。在此基础上 ,对粘弹性各向异性砂岩和页岩进行了模拟 ,得到相速度、衰减系数和品质因子随频率、方位和入射角的变化规律。模拟结果显示 ,3种波的品质因子和相速度在大于 10Hz的地震频带内随频率的变化基本保持不变 ;而在低频带 ,品质因子趋于无穷大 ,介质基本上接近弹性。纵波的衰减系数在地震频带内基本上呈线性变化 ,而横波的衰减系数在地震频带内除低频外基本保持稳定。

Characteristics analysis on wave field in linear viscoelastic HTI media

The constitutive relations for the linear visco-elastic HTI media are deduced. Firstly, probing the medium with a time-harmonic homogeneous plane wave gives the Christoffel equation. Then the formulas for slowness and complex velocities of the longitudinal wave and the slow and quick shear waves may be obtained from Christoffel equation. The simulation experiment on anisotropic sandstone and shale with linear visco-elasticity was carried out. It is found that the quality factor and phase velocity of the three waves were unchangeable with the change of frequency on the exploration seismic band with a frequency over 10 Hz. The quality factor changed infinitely in the seismic band with a low frequency. The attenuation factor of longitudinal wave was changing linearly, whereas the attenuation factor of the slow shear wave kept nearly constant with a low frequency on the exploration seismic band.